The world number one, champion at St Andrews in 2000, hardly put a foot wrong as he become only the second player after Jack Nicklaus to win each of the grand slam events at least twice.
Back to his very best form, the 29-year-old American fired a two-under-par 70 in breezy conditions on the Old Course to finish at 14-under 274.
He now stands third in the all-time listings for major winners, behind fellow Americans Nicklaus (18) and Walter Hagen
(11).
Impressively, the pace of his major successes is well ahead of Nicklaus. The Golden Bear, who made an emotional Open farewell at St Andrews two days ago, secured his 10th grand slam title when he was 32.
"This is as special as it gets, to complete my first career grand slam and then to complete the second both at the same place... at the home of golf," said a jubilant Woods.
"This is something you dream about. It doesn't get any sweeter than that.
"That's why I bust my butt so hard at home to get to this point," added Woods, who spent much of last year revamping his swing for the second time since turning professional in 1996.
"I've been criticised for years now, for the last couple of years. Why would I change my game? This is why.
BEST BALL-STRIKING
"First, second and first in the last three majors, that's why. I'm so excited to have my best ball-striking rounds when I need it the most, to hit the ball that solidly."
Leader from day one after opening with a 66, Woods was never headed during the week although his advantage was briefly cut to one on the last day when he bogeyed the par-four 10th after driving into a greenside pot bunker.
His playing partner Jose Maria Olazabal of Spain and Briton Colin Montgomerie had been his closest challengers but both fell away soon afterwards.
"Looking at that leaderboard anything could have happened... today was one incredible battle," said Woods, adding that he began the day with one of the best warm-up sessions of his life.
"I was hitting it so well," he said. "And I wanted to carry it to the golf course, and I did."
Twice U.S. Masters champion Olazabal dropped shots on 12, 13, 15 and 17 but birdied the last on his way to a 74 and a tie for third with Fred Couples (68) at eight under. Montgomerie's challenge ended with bogeys on 11, 13 and 16.
The 42-year-old Scot returned a 72 to secure second place at nine under, his best Open finish in 16 starts but only his second top-10.
It was his fourth runner-up placing at a major, and his first since he placed second in the 1997 U.S. Open at Congressional.
"The last couple of days have been amazing," said Montgomerie, who enjoyed passionate home support all week in his bid to make a major breakthrough.
PHENOMENAL SUPPORT
"Playing with Tiger yesterday was an experience. And today the crowd were phenomenal the whole way around. Even when they realised I wasn't going to win, they realised my job in hand was to try to finish second. They helped me to that cause.
U.S. Open winner Michael Campbell carded a 72 to finish in a six-way share of fifth at seven under, level with world number two Vijay Singh (72), Spaniard Sergio Garcia (73) and double U.S. Open champion Retief Goosen (74).
Two strokes clear of the field overnight, Woods held off the early challenge of his pursuers with birdies at the fifth, ninth, 12th and 14th sandwiched around a solitary bogey at the par-four 10th.
After picking up his first shot of the day at the par-five fifth, he missed an opportunity to forge three shots clear when he lipped out from six feet at the seventh.
However, he drove the green at the par-four ninth for his third birdie of the week there to reach the turn in two-under 34.
His stumble at the 10th, where he also tried to drive the green, was followed by further birdies at the 12th and 14th as he put daylight between himself and his rivals, none of whom were able to mount a sustained challenge.
He could afford a bogey at the notorious Road Hole, where he failed to reach the green in two, and a safety-first approach on the last left him with a short putt for par to complete a dominant display.
A strong finisher when leading or holding a share of the lead after 54 holes, Woods has now triumphed 37 times worldwide from 42 attempts.
His major record is perfect in that regard, winning all 10 of his titles after leading with one round to play.
Leading all-time career winners of professional major titles (country of origin U.S. unless stated otherwise):
18 - Jack Nicklaus
11 - Walter Hagen
10 - Tiger Woods
9 - Ben Hogan, Gary Player (South Africa)
8 - Tom Watson
7 - Bobby Jones, Harry Vardon (Britain), Gene Sarazen, Sam Snead, Arnold Palmer
6 - Lee Trevino, Nick Faldo
